I do.
Well, I will give you an answer. If large FCM are doing equity acquisition using CME instruments, i.e. hit bid on rate future and lift offer on index future, alternatively (sell cash bond and buy cash equity) then the HFT firm providing offer on the ES will need to lift offer in cash equities to perform the index arb.
This means that a larger book imbalance tilted to offer on listed cash market is just providing risk offset for HFT firms providing offer on ES.
Institutional buying is the other side of this trade, so the HFT arb group is heavy in cash offer and ES offer.
They lift offers in cash against filled offers on GLOBEX. This means that they need cash offers, and they also need the cash offers to be firm.